Robustness and sensitivity analysis of risk measurement procedures

Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ‘risk measure’ that summarizes the risk of the portfolio. We define the notion of ‘risk measurement procedure’, which includes both of these steps, and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between the subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property.